Assessing Supported Employment With Veterans With Felony Convictions and Mental Illness or Substance Abuse: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Assessing Supported Employment With Veterans With Felony Convictions and Mental Illness or Substance Abuse (NCT01629953), a randomized na study. The primary outcome is Employment.

2. Clinical Question

3. Trial Design

The registry record identifies NCT01629953 as a completed, randomized, parallel-group study. It lists the phase as NA and masking as none. The sponsor was the VA Office of Research and Development. The recorded start date is 2011-10-31 and the primary completion date is 2016-10-31. Enrollment is listed as 140.

The comparison was between Group Based Vocational Rehabilitation and the Supported Employment Condition. The first arm is described as a group vocational intervention. The second is described as that intervention plus supported employment. The registry summary says that the study continued work on vocational services for veterans with histories of felony convictions and mental health or substance abuse difficulties. It describes supported-employment components as ongoing follow-up, treatment-team coordination, and community-based assistance. Further operational details, including how these components were implemented, are not reported in the registry record.

The posted primary outcome is a count of participants finding work within 6 months. The arm-level outcome denominators are 38 and 46, with 8 and 21 participants, respectively, counted as finding work. Those denominators differ from the overall enrollment listed in the registry record; the record does not explain the difference, identify the analysis population, or describe participant flow into the outcome analysis. The adverse-event record uses different at-risk counts, which are discussed separately.

The registry record does not report the randomization sequence method, allocation concealment, recruitment sites, detailed eligibility criteria, or the trial's original sample-size justification. It also does not give the protocol's full statistical analysis plan or the dates when individual participants were followed. These gaps limit how much can be concluded about implementation and analysis from the registry entry alone.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Employment, measured over within 6 months.

The primary endpoint counts participants who found work within 6 months. It is a binary outcome at the participant level: each participant either contributes to the count of those finding work during the specified period or does not. The registry describes the outcome as the number of veterans finding work within 6 months and gives the unit as participants.

This endpoint addresses an employment outcome that is directly connected to the vocational-service question. A count can be translated into a proportion within an arm for interpretation, and the posted comparison reports arm-level proportions as 0.210 for Group Based Vocational Rehabilitation and 0.457 for the Supported Employment Condition. The reported risk difference expresses the contrast in those proportions on an absolute scale. These summaries describe the endpoint as recorded; they do not provide details about how employment was verified, what types of work qualified, or how participants without follow-up information were handled. Those details are not reported in the registry record.

Using a defined follow-up period gives the outcome a time boundary: the endpoint concerns employment within 6 months, not employment at any later time. The registry record does not report additional characteristics of employment, such as duration, hours, or job quality. As a result, the endpoint captures whether work was found within the stated period, rather than the full experience of employment.

7. Results Posted in the Registry

• Supported Employment Condition: 45.7% (21/46) versus 21.1% (8/38) on control; risk difference 24.6 percentage points (95% CI 5.2 to 44.0), risk ratio 2.17 (1.09–4.33); unadjusted two-proportion z-test p = 0.018.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is a binary participant outcome: finding work within 6 months. For a binary outcome, each arm can be described by the number with the event and the number in the arm used for that analysis. The posted counts are 8 of 38 for Group Based Vocational Rehabilitation and 21 of 46 for the Supported Employment Condition. The registry reports proportions of 0.210 and 0.457, respectively. These are arm-level descriptions, not separate tests of each arm.

What does the risk difference describe?

The risk difference subtracts one arm's event proportion from the other arm's event proportion. It is an absolute-scale measure: it describes the change in the proportion of participants finding work associated with the contrast between the two arms. The registry reports a risk difference of 0.246 for the Supported Employment Condition compared with Group Based Vocational Rehabilitation. It is not a relative increase and should not be confused with the risk ratio or odds ratio. The absolute scale can be useful because it keeps the comparison tied to the event proportions observed in the two arms.

How do the relative measures differ?

The risk ratio compares the event proportions as a ratio. The posted risk ratio is 2.168, with a 95% confidence interval from 1.086 to 4.331. The odds ratio compares the odds of the event between arms rather than comparing the proportions directly. The posted odds ratio is 3.15, with a 95% confidence interval from 1.192 to 8.326. Risk ratios and odds ratios are distinct measures, even though both are relative comparisons. Their numerical values should not be treated as the same quantity. For interpretation, it is helpful to retain the arm counts and proportions alongside each relative measure.

What does a confidence interval add?

A confidence interval gives a range of values compatible with the observed data and the method used to calculate the interval. It communicates uncertainty around an estimate, rather than only presenting a single point estimate. The 95% confidence interval for the risk difference is 0.052 to 0.440. The posted intervals for the risk ratio and odds ratio are also reported with their respective estimates. The interval's width reflects precision: wider intervals leave more uncertainty about the size of the contrast. A confidence interval does not guarantee that the true effect lies within its endpoints, and it does not account for limitations that are not represented in the statistical model, such as missing outcome information or differences in implementation.

What does the p-value test?

The registry reports an unadjusted p-value of 0.018. In general, a p-value measures how unusual data at least as incompatible with a null hypothesis would be if that null model and the test assumptions held. It is not the probability that a treatment effect is real, and it does not tell readers whether an effect is important. An unadjusted p-value is calculated without an adjustment for other comparisons or covariates, but the registry record does not report the full test specification or whether any adjusted analysis was also performed. The value should therefore be described as the unadjusted result posted in the record.

Why do analysis choices matter?

Statistical interpretation depends on which participants were included, how missing outcomes were treated, whether the comparison was prespecified, and whether other analyses were conducted. The registry record does not report the analysis population, a missing-data method, an adjusted model, or a multiplicity procedure. It also does not report a detailed statistical analysis plan. Without those details, readers cannot fully evaluate whether the posted estimates correspond to an intention-to-treat analysis, a complete-case analysis, or another approach. No particular approach should be inferred from the randomized design alone.

Randomization is the stated allocation design, but the registry entry does not report the sequence-generation or concealment procedures. Masking is listed as none. In general, a randomized comparison is designed to reduce systematic differences between groups at assignment, while lack of masking can matter for how services are delivered and how outcomes are assessed. The outcome is finding work, but the record does not say how employment status was determined or whether outcome assessment was independent of treatment delivery. These are questions about study conduct; they cannot be resolved from the effect estimates alone.

For binary outcomes, the event counts and denominators are essential context. The primary-outcome denominators are 38 and 46, while the registry's overall enrollment is 140. The record does not explain the relationship between these figures. That gap affects interpretation of representativeness and missingness, but it does not justify assuming why they differ. The appropriate reading is to retain the posted denominators and recognize that participant flow and outcome availability are not reported in the registry record.

10. Confidence Intervals and Precision

The point estimate for the primary comparison is a risk difference of 0.246. Its 95% confidence interval ranges from 0.052 to 0.440. The interval is the main indication of the estimate's statistical precision: it shows that the data do not pin the contrast down to a single value. The range includes positive differences of varying size, so the point estimate should not be mistaken for an exact measure of the contrast that would apply in every setting.

The lower endpoint is above zero, while the upper endpoint is considerably farther from zero. For this comparison, the interval is compatible with a smaller positive difference as well as a larger one. The reported confidence interval for the risk ratio is 1.086 to 4.331, and for the odds ratio it is 1.192 to 8.326. These intervals also communicate uncertainty on their respective scales. Because the scales differ, their endpoints cannot be compared directly with the endpoints of the risk-difference interval.

Precision is influenced by the amount of information in the analyzed groups and the variation in outcomes. The primary-outcome denominators are 38 and 46, and the event counts are 8 and 21. Those data support an estimate, but the intervals remain important context for judging its uncertainty. Confidence intervals account for sampling variation under their calculation method; they do not resolve possible concerns about missing outcomes, outcome assessment, or the analysis population. Those aspects are not reported in the registry record.

The unadjusted p-value is 0.018, but the p-value and confidence interval serve different interpretive purposes. The p-value summarizes compatibility with a null model under test assumptions, whereas the interval conveys a range of plausible effect values under the interval method. Neither measure alone establishes the importance, generalizability, or practical implications of the estimated difference.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size figures are planning illustrations based on the observed effect, not the trial's original sample-size calculation. They are participants per arm, not total events. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The calculation considers detecting a stated fraction of the observed effect. The original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the number of participants per arm in a hypothetical future design that would have 80% power under the listed assumptions and chosen effect size. The 90% power column gives the corresponding number per arm for 90% power. Power is the probability, under a specified assumed effect and model, of detecting an effect at the chosen significance level. These columns are planning aids; they do not describe the probability that this completed trial detected an effect, and this is not observed power.

The displayed planning scenarios use 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. In the listed scenarios, the per-arm requirements for 80% power are 57, 97, and 205, respectively; for 90% power they are 76, 129, and 273, respectively. The pattern illustrates a general planning principle: smaller effects are harder to distinguish from random variation, so detecting them at the same power generally requires more participants.

These figures depend on assumptions that may not match the original trial design or a future study. In particular, they use an effect estimated from the posted results, and such an estimate is uncertain. The figures do not account for any design features beyond the stated assumptions. Readers should treat them as illustrations of how sample size changes with the assumed effect and target power, not as evidence that any particular sample size is sufficient for a new study.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.211; treatment proportion p₁ = 0.457; average p̄ = 0.334.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6668 = 1.3068.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6437 = 0.5417.
4. n = (1.3068 + 0.5417)² / (0.2460)² = 56.5, rounded up to 57 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.210526315789474                          # control proportion
p1 <- 0.456521739130435                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1629953)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 57 (80% power), 76 (90% power)
 75% of observed effect: n per arm = 97 (80% power), 129 (90% power)
 50% of observed effect: n per arm = 205 (80% power), 273 (90% power)
power.prop.test: 56.5 
Simulated power at n = 57 per arm: 0.816 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The registry record lists no posted analyses. It reports a primary endpoint and a comparison, but does not report a detailed analysis plan explaining how the primary comparison was selected, whether other comparisons were planned, or whether additional analyses were conducted. The record also does not report a multiplicity adjustment. When several outcomes, time points, or comparisons are examined, the chance of at least one apparently unusual result can increase; adjustment or a prespecified hierarchy can address that issue, depending on the analysis plan. Whether either approach was used in this trial is not reported in the registry record.

The unadjusted p-value of 0.018 should therefore be understood as the reported unadjusted result. It is not possible to determine from the registry entry whether it was the only inferential test, whether it was selected after examining other results, or whether an adjusted result exists. No assumption should be made that multiplicity was handled or ignored beyond what is explicitly reported.

The registry lists enrollment as 140, while the primary outcome uses denominators of 38 and 46 in the two arms. It does not report participant flow, the analysis population, or reasons that the primary-outcome denominators differ from overall enrollment. The record also does not describe how participants without an observed employment outcome were handled. Thus, it is not possible to establish whether the posted comparison includes all randomized participants or only participants with outcome data.

In general, missing-data methods can affect estimates when the probability of an outcome being observed is related to participant characteristics or outcomes. The registry record does not report the amount or pattern of missing primary-outcome data or any imputation or sensitivity analysis. It also does not report an intention-to-treat statement or a per-protocol analysis. These gaps limit assessment of the potential influence of missingness and analysis-population choices; they do not establish that any particular bias occurred.

The record identifies randomization but does not report how the sequence was generated or concealed. It also lists masking as none. Details about outcome ascertainment and assessment are not reported in the registry record. The absence of those details means the statistical result cannot be fully appraised as a complete analysis report, even though arm-level counts and comparative estimates are posted.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The adverse-event record lists 52 participants at risk for serious adverse events in Group Based Vocational Rehabilitation and 60 in the Supported Employment Condition. It reports 0 serious adverse events affecting participants in each group. For other adverse events, the listed at-risk counts are also 52 and 60, with 0 affected in each group. The record lists 1 death in Group Based Vocational Rehabilitation and 5 in the Supported Employment Condition.

These figures describe the counts recorded for each category and the stated at-risk groups. The death counts are reported separately from the serious-adverse-event and other-adverse-event affected counts. The registry does not provide further detail about the deaths, their timing, their causes, or whether they were considered related to an intervention. It also does not report serious adverse-event terms. The absence of affected participants in the posted adverse-event categories should not be read as proof that no events occurred outside the recorded definitions or observation period.

The adverse-event at-risk denominators differ from the primary-outcome denominators. The registry record does not explain that difference, provide follow-up duration for adverse-event ascertainment, or describe completeness of reporting. Accordingly, the figures are best read as registry-recorded counts rather than as a comprehensive comparison of safety risk. They do not support conclusions about the cause of deaths or about comparative safety.

15. What the Result Does, and Does Not, Mean

The posted primary result describes more participants finding work within 6 months in the Supported Employment Condition than in Group Based Vocational Rehabilitation: 21 of 46 compared with 8 of 38. The estimated risk difference is 0.246, with a 95% confidence interval from 0.052 to 0.440. The registry also reports relative measures, including a risk ratio of 2.168 and an odds ratio of 3.15. Together, these statistics describe the observed comparison and its sampling uncertainty.

The result does not, by itself, establish that supported employment caused the difference. Randomized allocation is recorded, but the entry does not report details of allocation procedures, analysis populations, missing outcome handling, or outcome assessment. The registry record also does not explain why the primary-outcome denominators differ from the overall enrollment of 140. Those issues matter when assessing how closely the posted estimate represents the planned randomized comparison.

The endpoint concerns finding work within 6 months. It does not measure all dimensions of employment or the longer-term employment experience. The registry does not report definitions of qualifying work, the method used to verify employment, job duration, hours, or job quality. Nor does the posted comparison establish whether the result would apply to veterans outside the population described in the summary, to other service settings, or to other intervention implementations.

The unadjusted p-value of 0.018 is one component of the statistical report, not a complete statement of evidence. The confidence interval indicates that the estimated absolute difference has uncertainty, and the registry record does not report multiplicity procedures or a full analysis plan. No medical recommendation follows from these data alone. The result should be read as a registry-posted comparison of the recorded outcome, with the stated denominators and reporting limitations.

16. Why This Trial Matters Statistically

This trial is statistically instructive because it places a binary employment outcome in a randomized, parallel-group comparison and reports both arm-level counts and several effect measures. The counts and proportions make the observed outcome transparent, while the risk difference, risk ratio, and odds ratio present the contrast on absolute and relative scales. Reading these measures together helps avoid relying on a single summary whose scale may be unfamiliar or incomplete for a particular question.

The confidence intervals are also central. A point estimate such as 0.246 is compact, but it does not convey how much uncertainty remains. The interval from 0.052 to 0.440 makes that uncertainty visible and prevents treating the estimate as exact. The relative-effect intervals provide a further reminder that estimates can be imprecise even when a single p-value appears small. Statistical significance and precision are related but are not identical concepts.

The registry record also illustrates why denominators and reporting completeness matter. Overall enrollment is 140, whereas the primary-outcome comparison uses arm denominators of 38 and 46. Without participant flow and analysis-population details, readers cannot resolve that difference. Likewise, the absence of a reported analysis plan, missing-data method, and multiplicity procedure limits independent appraisal of the inferential result. Those are not minor details when interpreting a trial's estimates.

Finally, the planning illustrations distinguish an effect estimate from a future design decision. The listed participant requirements vary with the fraction of the observed effect selected for planning and with the target power. This demonstrates a general statistical principle: assumptions about the effect to detect influence sample-size planning. It does not reveal the rationale for the original enrollment or provide an evaluation of the trial's observed power.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

Several trial-specific details needed for a fuller appraisal are not reported in the registry record. The record lists overall enrollment as 140 but gives primary-outcome denominators of 38 and 46. It does not provide a participant-flow account or explain why these figures differ. Without that information, it is not possible to determine how many randomized participants contributed to the primary comparison, what happened to those not represented in the outcome denominators, or whether the result reflects a particular analysis population.

The registry entry does not describe how employment was defined or assessed, whether work status was verified, or how participants without outcome information were classified. Those details are particularly relevant because the endpoint is a count of participants finding work within 6 months. The record does not report the durability or characteristics of employment, so the posted endpoint should not be interpreted as covering those aspects.

Although allocation is listed as randomized, the sequence-generation and concealment procedures are not reported. Masking is listed as none, and the registry record does not say who assessed employment outcomes or whether assessment was independent of intervention delivery. These reporting gaps do not demonstrate that bias occurred, but they limit assessment of how it might have been prevented or evaluated.

The record does not report the original sample-size justification, a detailed statistical analysis plan, adjustment for multiplicity, or handling of missing data. It also does not provide a fuller account of intervention delivery or adherence. The adverse-event entry lists at-risk counts and events but does not give event timing, causes of death, or detailed adverse-event terms. These limitations restrict interpretation of both the primary comparison and the safety counts, and they should be kept distinct from the uncertainty represented by the confidence intervals.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Assessing Supported Employment With Veterans With Felony Convictions and Mental Illness or Substance Abuse — NCT01629953.
• Registry record last updated 2019-06-17; status last verified 2019-06.
• Results first posted 2018-05-22.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

NCT01629953 is listed as a completed, randomized, parallel-group, unmasked study sponsored by the VA Office of Research and Development. Its enrollment is listed as 140. The comparison is Group Based Vocational Rehabilitation versus the Supported Employment Condition, which adds supported employment to the group vocational intervention. The registry summary concerns vocational services for veterans with histories of felony convictions and mental health or substance abuse difficulties.

The primary outcome counts participants finding work within 6 months. The posted counts are 8 of 38 in Group Based Vocational Rehabilitation and 21 of 46 in the Supported Employment Condition. The reported risk difference is 0.246, with a 95% confidence interval from 0.052 to 0.440; the unadjusted p-value is 0.018. The record also lists risk-ratio and odds-ratio estimates with confidence intervals.

Important analysis details, including participant flow, the analysis population, missing-data handling, and the original sample-size justification, are not reported in the registry record. Adverse-event counts are recorded separately, including 0 serious adverse events in each group and death counts of 1 and 5, respectively. These results should be interpreted in light of the registry's stated denominators and reporting limitations.